With the expansion of renewable energy's contribution to the energy mix, balancing the electricity grid is becoming increasingly challenging. Alongside other solutions, Power-to-Hydrogen concepts are gaining significant interest. In this paper, the “Task 38”, initiated by the Hydrogen Implementing Agreement of the International Energy Agency, presents the first of a two-step literature review regarding Power-to-Hydrogen and Hydrogen-to-X concepts with a focus on prospective market and economic potential. The study reveals a large scope of literature that shows a considerable variety of suggested implementation schemes. The transportation sector is identified as the most promising consumer market. Hydrogen-to-Gas pathways will require subsidies in order to be profitable. Hydrogen-to-Power becomes an economically promising option in the context of systems with high shares of renewables and a need for longer-term storages. Additionally, key enablers for Power-to-Hydrogen concepts are identified; namely support policies, concurrently with ongoing progress on the development and implementation of industry standard.